I'm having trouble getting the right answer for a problem, I'm hoping that by posting my work someone can help me figure out where I've gone wrong.
A two-liter soft drink bottle can withstand a pressure of 5 atm. Half a cup [approximately 120 mL) of ethyl alcohol C2H5OH, (d= 0.789 g/mL) is poured into a soft drink bottle at room temperature. The bottle is then heated to 100 degrees C [3 sig figs], changing the liquid alcohol to a gas. Will the soft drink bottle withstand the pressure, or will it explode?
My work:
P= nRT/V
to find n:
.789 g/mL x 120 mL = 94.68 g = xmol x 46.08 g/mol
x= 2.055 mol
(2.055 mol x .08206 L x atm/mol x K x 373.15 K) / 2 L
= 31.46 atm
This number seems high to me. Am I setting up the problem correctly?
You have done it correctly, if the assumption that all of the ethyl alcohol vaporizes is valid. The way they worded the question, you cannot say for sure if they expect you to assume that it all evaporates. If it does, it is ok to use the ideal gas law, as you have done.
However, you need to consider the vapor pressure of alcohol as a function of temperature to see if it can all evaporate. Extrapolating from vapor pressure data I can find, and using a log P = a + b/T fit, it is appears that the vapor pressure of C2H5OH is about 2 atm at 100 C. (It is 1 atm at 78.5 C.) This means that the vapor pressure in the bottle will rise to a temperature insufficient to break the bottle, and that most of the alcohol will remain in liquid form.
You may have copied the question wrong because I had the same one for homework, only d=0.789g/L instead of g/mL. That error would account for your unusually high number
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To verify this, you can calculate the pressure inside the bottle using the ideal gas law and compare it to the maximum pressure the bottle can withstand (5 atm).
Assuming that the alcohol completely vaporizes, you can use the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
You have already determined the number of moles of ethyl alcohol to be 2.055 mol.
Next, convert the temperature to Kelvin:
100 degrees C + 273.15 = 373.15 K
Now plug in the values into the equation:
P * 2 L = 2.055 mol * 0.08206 L * atm/mol * K * 373.15 K
Simplifying the equation:
P = (2.055 mol * 0.08206 L * atm/mol * K * 373.15 K) / 2 L
Calculating this, you get:
P = 31.46 atm
Comparing this to the 5 atm maximum pressure the bottle can withstand, it is clear that the pressure inside the bottle is higher than what the bottle can tolerate.
Therefore, based on your calculations, if all the alcohol were to vaporize, the soft drink bottle would explode under the increased pressure. However, considering the approximated vapor pressure of alcohol at 100 degrees C, it is likely that most of the alcohol will remain in liquid form, and the bottle will not explode.
To calculate the pressure inside the bottle, you need to consider the vapor pressure of the ethyl alcohol at the given temperature. Vapor pressure is the pressure exerted by the vapor when a substance is in equilibrium with its liquid state at a particular temperature.
In this case, you can estimate the vapor pressure of ethyl alcohol at 100 degrees C using the information you have. You mentioned that the bottle can withstand a pressure of 5 atm, so if the vapor pressure exceeds this value, the bottle will not be able to withstand it and may explode.
To estimate the vapor pressure, you can use experimental data or vapor pressure charts for ethyl alcohol. However, since you do not have that information, you can make an estimation based on the data you do have.
You mentioned that the density of ethyl alcohol is 0.789 g/mL. From this, you calculated the number of moles of ethyl alcohol using its molar mass of 46.08 g/mol. You obtained a value of 2.055 mol.
Now, to estimate the vapor pressure, you need to consider the equilibrium between the liquid and gaseous states at 100 degrees C. However, since the concentration of ethyl alcohol is not given, the calculation you performed assumes that all the alcohol evaporates, which may not be accurate.
To get a better estimate, you can use the fact that the vapor pressure of a substance is related to its concentration. The mole fraction of ethyl alcohol in the vapor phase can be related to the total pressure using Raoult's law:
P_vap = X_ethanol * P_ethanol
Where P_vap is the vapor pressure, X_ethanol is the mole fraction of ethyl alcohol in the vapor phase, and P_ethanol is the vapor pressure of ethyl alcohol at a given temperature.
Given that the bottle can withstand a pressure of 5 atm, you need to determine if the vapor pressure of ethyl alcohol at 100 degrees C is greater than this value. If it is, the bottle will not be able to withstand the pressure, and there is a risk of explosion.
In summary, to accurately determine whether the bottle will withstand the pressure or explode, you need to consider the vapor pressure data of ethyl alcohol at the given temperature. Without this information, it is difficult to make a definitive conclusion. However, based on extrapolated data, it seems that the vapor pressure of ethyl alcohol at 100 degrees C is approximately 2 atm, which is below the bottle's pressure threshold. This suggests that most of the alcohol will remain in liquid form, and the bottle is likely to withstand the pressure without exploding.